The plerionic Composite-type Supernova remnants (SNR's) represent a class of SNR's observed to have two components: emission from the SNR shell resulting from shock-heated ISM, and emission from a plerion associated with a compact object, powering the SNR and causing its center-filled morphology. CTB 8O & W5O are two 'unusual' plerionic supernova remnants (SNR's), whose properties are to a large extent associated with the emission from their powering engines responsible for their plerionic character. Their X-ray emission is the key to a better understanding of their unusual properties. I have analyzed the emission from CTB80 and its associated pulsar with the ROSAT satellite sensitive in the 0.1-2.4 keV band. I have also studied W50 with ROSAT and with ASCA, thus covering the 0.1-10 keV band. CTB 80 contains a 40 millisecond isolated pulsar, PSR1951 + 32, emitting non-thermal X-rays by magnetospheric emission, powering a ≤1&sp;prime compact nebula, and surrounded by a ~5&sp;prime synchrotron nebula extending east of the pulsar. With the ROSAT PSPC, a large ≤1&sp;prime emission region is also detected in the hard energy of the spectrum away from SS433. The inner X-ray jets out to the base of the radio 'ears' have a very hard spectrum, found in the combined ROSAT and ASCA energy band (0.1-10 keV), with evidence of production of very high (TeV) cosmic rays. However, at the radio 'ears', where the jets interact with the surrounding medium, the emission was considerably softer. Correlating the X-ray maps of CTB80 and W50 with their maps at other wavelengths, their unusual morphology can be interpreted in the light of interaction between the wind or the jets from their engines with the surrounding SNR shell, which seems to be expanding in a low-density ISM.